Hector Permafrost
Alexey N. Shiklomanov
Ben Bond-Lamberty
Ben Kravitz
Corinne Hartin
05 February, 2020
Abstract
Text of abstract
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## intersect, setdiff, setequal, union## Loading hector1 Introduction
Permafrost—soil that continuously remains below 0°C for at least two consecutive years—underlies an area of 22 (± 3) million km2, roughly 17% of the Earth’s exposed land surface (???), and contains an estimated 1300 (1100-1500) Pg of organic carbon (Hugelius et al., 2014). Recent increases in global air temperature (IPCC, 2013), which are amplified at high latitudes (???), have resulted in widespread permafrost thaw (???), and simulations from variety of climate and land surface models across a wide range of scenarios suggest that this trend will continue into the future (Chadburn et al., 2017; Koven et al., 2013). Permafrost thaw can dramatically alter surface terrain and hydrology (???; ???; ???), with adverse consequences for human infrastructure in permafrost regions (Anisimov and Nelson, 1997; Larsen et al., 2008; Nelson et al., 2002). Moreover, as permafrost thaws, this carbon becomes available to microbes for decomposition, resulting in the production of CO2 and CH4 (???; Brown and Romanovsky, 2008; Romanovsky et al., 2010) that could lead to further warming (Koven et al., 2011; Schuur et al., 2015). Accounting for this permafrost carbon-climate feedback generally increases projections of greenhouse gas concentrations and global temperatures (REFS) and increases estimates of the economic impact of climate change (Chen et al., 2019; Hope and Schaefer, 2015; Yumashev et al., 2019).
The higher carbon emissions associated with warming-driven permafrost thaw may be offset by increases in primary productivity. Some studies based on meteorological tower measurements of carbon flux and optical remote sensing suggest that high-latitude ecosystems (mainly tundra and boreal forest) remain carbon-neutral or are even a small net carbon sink (???; ???). However, other studies, based on different sets of flux measurements and airborne gas sampling, suggest that the high-latitude regions are a net carbon source (???; ???; ???). The uncertainty in the net high-latitude carbon flux may be driven by the heterogeneity of high-latitude landscapes in terms of vegetation cover, soil properties, topography, and many other factors known to affect both the rate of permafrost thaw and the subsequent carbon flux (???; ???; ???; Grant et al., 2019a, 2019b; Turetsky et al., 2002; Wickland et al., 2006). This uncertainty is also present in recent permafrost modeling studies (Burke et al., 2017; Harp et al., 2016; Ito et al., 2016; Qian et al., 2010).
Land surface models are expensive to run, making it challenging to use them for uncertainty quantification and exploration of alternative policy scenarios. Simple climate models are an alternative. (More on simple climate models). (More on permafrost in simple climate models).
Hector (???; Hartin et al., 2015). In this study, we implement a simple representation of permafrost thaw and evaluate its consequences for global climate in Hector.
2 Methods
2.1 Model description: Hector
Hector (Hartin et al., 2015, p.@hartin_2016_ocean,). Simple climate model.
(TODO: More details on terrestrial C cycle in Hector). The default heterotrophic respiration (\(R\)) scheme for a pool \(p\) (detritus or soil) in Hector:
\[ R_{p} = C_p \times f_p \times Q_{10} ^ \frac{T}{10} \]
2.2 Hector permafrost sub-model
The general principle is that permafrost constitutes an additional reserve of soil carbon that, because it is frozen, is inaccessible to microbes. As permafrost thaws and some fraction of this carbon becomes accessible to microbes, it is transferred from the frozen permafrost pool to the standard soil C pool, where it is decomposed by Hector’s standard decomposition routine. Let \(C_{pf}[t]\) be the permafrost C pool and \(C_{s}[t]\) be the soil C pool at time \(t\) (both in units of Pg C), and let \(\Delta C_{pf}[t]\) be the change in the permafrost C pool at time \(t\). The C consequences of permafrost thaw can therefore be represented as:
\[ C_{pf}[t] = C_{pf}[t-1] - \Delta C_{pf}[t] \]
\[ C_{s}[t] = C_{s}[t] + \Delta C_{pf}[t] \]
Let \(C[0]_{pf}\) be the initial size of the permafrost C pool (Pg C) and \(\Phi[t]\) be the fraction of permafrost remaining (in arbitrary area or volume units) at time \(t\). Assuming a uniform permafrost C density, \(\Delta C_{pf}[t]\) can be expressed as:
\[ \Delta C_{pf}[t] = \Delta \Phi[t] C_{pf}[t-1] \]
To a first approximation, \(\Phi[t]\) is a function of air temperature (\(T[t]_{air}\)). Kessler (2015) assume this relationship is linear. However, because the permafrost area fraction is, by definition, bounded by zero (and 11), and because deeper permafrost thaws more slowly than shallow permafrost, we use a negative logistic relationship instead:
\[ \Phi[t] = 1 - \left( 1 + a \exp\left( b * T_{air}[t] \right) \right) ^ c \]
where \(a\), \(b\), and \(c\) are model parameters. The change in frozen fraction at a given time step, \(\Delta \Phi[t]\), is given by:
\[ \Delta \Phi[t] = \max(\Phi[t] - \Phi[t-1], 0) \]
In other words, permafrost thaw is permanent – once it thaws, it does not re-freeze, even if the temperature drops.
For globally-averaged permafrost, \(a = 2.371\), \(b = -0.676\), and \(c = -3.685\) to most closely reproduce the rate of 0.172 K\(^{-1}\) reported by Kessler (2015) over the range of 0.82 to 4 K above the pre-industrial baseline.
Figure 1: Fraction of permafrost thaw as a function of change in global annual mean air temperature since pre-industrial (1750).
2.3 Configuration
Initial permafrost C is set to 1035 Pg C.
3 Results
3.1 Effect of permafrost C
Figure 2: Effect of permafrost C emissions on scenarios.
4 Discussion
Rate of permafrost C release also depends on soil moisture conditions – drier soils release C much faster (“carbon bomb”) than wetter soils (“carbon fizz”) (Elberling et al., 2013). Moisture will also affect the balance of aerobic (CO2 release) vs. anaerobic (CH4) C release (Turetsky et al., 2002), to the extent that unclear if anaerobic (wet) areas are C sources or sinks (Wickland et al., 2006). Effects of permafrost thaw on soil moisture are a complex hydrological problem – drainage very sensitive to local (micro-)topography (Wickland et al., 2006). So will vegetation cover (Wickland et al., 2006).
Temperature amplification of permafrost carbon feedback (by 2100) 0.02 to 0.36 °C (Burke et al., 2013; Schneider von Deimling et al., 2015, 2012), or 0.1 to 0.8 °C in (MacDougall et al., 2012, 2013), or 10-40% of peak temperature change (Crichton et al., 2016), or 0.2 to 12% (Burke et al., 2017).
Permafrost carbon has greater impact at lower emissions scenarios (Burke et al., 2017; MacDougall et al., 2012, 2013) .
5 Conclusion
6 Acknowledgments
Funded by EPA grant XXX. Cyberinfrastructure support from Pacific Northwest National Laboratory (PNNL).
7 Miscellaneous notes
7.1 Permafrost emissions scenarios
Digitized scenarios from (Schaefer et al., 2011).
SiBCASA model predictions of CO2 emissions (permafrost respiration; \(R_{pc}\); note – no methane!) through 2300.
These results were digitized using WebPlotDigitizer (https://apps.automeris.io/wpd/), and interpolated to annual resolution (using R stats::spline function).
Digitized scenarios from (Hope and Schaefer, 2015). CO2 and CH4 emissions from SiBCASA model.
(Schuur et al., 2009) – Estimate 0.8 - 1.1 Pg C yr-1.
Back-of-the-envelope estimates from (Zimov et al., 2006): - 500 Gt C in loess that could be completely emitted by 2100 (plus other C sources). - 10-40 g C m-3 day-1 off the bat, slowing down to equilibrium (?) rate of 0.5-5 g C m-3 day-1 for several years. Combine with data on permafrost spatial extent, density, etc. to generate estimates (but can back-calculate from 500 Gt C above?)
7.2 Parameter calibration
We used the BayesianTools R package (Hartig et al., 2019) for all parameter calibration.
The outputs of these calibrations are joint posterior distributions of parameters and their covariances, from which we sample for the sensitivity analysis.
For global parameters, we used the following likelihood:
\[ \log(L) = \sum_s Normal(Hector(\beta, Q_{10}, s) | CMIP5(s), \sigma) \]
where \(s\) is one of the four representative carbon pathways (RCPs), \(CMIP5(s)\) are the CMIP5 global mean outputs for the corresponding variables, and \(\sigma\) is the model error (estimated during the fit). We also used the resulting distributions for \(\beta\) and \(Q_{10}\) for the non-permafrost biome in cases 2 and 3. We feel this is appropriate because the CMIP5 models against which these parameters are calibrated do not include permafrost C feedbacks.
For case 2, we calibrated the permafrost-specific \(\beta\) and \(Q_{10}\) against various literature sources, including:
- Land surface model simulations (Burke et al., 2017; Hope and Schaefer, 2015; Schaefer et al., 2011).
- Try to calibrate against NPP and soil respiration if possible
- Literature surveys (Schaefer et al., 2014)
- Warming experiments (Wickland et al., 2006)
- TODO: Others?
Some of these are time series, while others are individual estimates at particular points in time. To give them equal weight in the likelihood, we down-weight the time series likelihoods by the number of time steps.
We derived a distribution for the Arctic warming factor from TODO.
TODO: Table and multi-panel figure of input datasets.
For the \(\alpha\) and \(\phi\) parameters in case 3, we looked at the literature on permafrost methane emissions (e.g., Wickland et al., 2006).
7.3 Other notes
Frozen carbon residence time (FCRt) from (Burke et al., 2017):
\[ FCRt = FCRt0 * exp(-\Delta T / \Gamma) (for \Delta T > 0.2 °C) \]
- \(FCRt_0\) (years) reflects the stability of permafrost C (length of time that permafrost C is stable when \(\Delta T = 0\))
- \(\Gamma\) – decay term (°C); temperature change at which “the number of years taken for all of the old permafrost C to be emitted reduces to 1/e of its initial value”
Other Hector parameters to consider.
| Variable | INI name | Description | Value |
|---|---|---|---|
| \(f_{nv}\) | f_nppv |
Fraction of NPP C transferred to vegetation | 0.35 |
| \(f_{nd}\) | f_nppd |
Fraction of NPP C transferred to detritus | 0.60 |
| \(f_{nd}\) | Fraction of NPP C transferred to soil | 0.05 | |
| \(f_{lv}\) | f_lucv |
Fraction of LUC change flux from vegetation | 0.10 |
| \(f_{ld}\) | f_lucd |
Fraction of LUC change flux from detritus | 0.01 |
| \(f_{ls}\) | Fraction of LUC change flux from soil | 0.89 | |
| \(f_{ds}\) | Fraction of detritus C that goes to soil | 0.60 | |
| \(f_{rd}\) | Fraction of respiration C to detritus | 0.25 | |
| \(f_{rs}\) | Fraction of respriation C to soil | 0.02 |
According to (Hartin et al., 2015), these were selected to be “generally consistent with previous simple earth system models (e.g., Meinshausen et al., 2011)”.
7.3.0.0.1 pagebreak
8 References
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9 Appendix
Figure 3: Figure 1: Input parameter distributions for global Hector.
Figure 4: Figure 2: Input parameter distributions for Hector with biomes.
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#> P ── Loaded and on-disk path mismatch.The current Git commit details are:
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#> Head: [9ab788d] 2020-02-05: More revisions to introductionTechnically, permafrost area could increase in the case of cooling temperatures, and therefore the area fraction could be greater than 1. However, because even the most aggressive climate action scenarios show temperatures that stabilize above year 2000, we assume that permafrost area will never grow more than the starting value.↩︎
Kessler (2015) report this as temperature change from year 2000. 0.8 K is the warming since pre-industrial as estimated by the default Hector configuration.↩︎